Mass of information

Let's say I encode all the information in some book in a light beam. Then I put a black hole in the way of the beam. Mass and information of the black hole increase as the beam plunges in the black hole.

But what if the black hole is moving very fast parallel to the beam? In this case the rest mass of the black hole may increase very little as the beam goes into the black hole.

There must be some mechanism that prevents us to dump information into a black hole without increasing its mass by a sufficient amount.

But what if the black hole is moving very fast parallel to the beam? In this case the rest mass of the black hole may increase very little as the beam goes into the black hole.

In this case it is natural to view the system in the frame of reference in which the black hole does not move. In this frame the beam still travels with the velocity of light, but it has a very long wavelength. The long wavelength implies two things: i) that the beam has a low density of energy, and ii) that the beam has a low density of information. I think that i) and ii) together answer your question.

In this case it is natural to view the system in the frame of reference in which the black hole does not move. In this frame the beam still travels with the velocity of light, but it has a very long wavelength. The long wavelength implies two things: i) that the beam has a low density of energy, and ii) that the beam has a low density of information. I think that i) and ii) together answer your question.

I don't see how that answers the question.

By choosing a suitable frame, energy of a light pulse can be as low as desired. But entropy of said light pulse is the same in all frames. If a small black hole absorbs a light pulse with high entropy and low energy, we have a problem of entropy decreasing in the universe.

By choosing a suitable frame, energy of a light pulse can be as low as desired. But entropy of said light pulse is the same in all frames. If a small black hole absorbs a light pulse with high entropy and low energy, we have a problem.

If you make the pulse to have a very small energy, it will have a very large wavelength. If the wavelength is larger than the size of the black hole, then the black hole cannot absorb it. I think this is the mechanism you are looking for.

If you make the pulse to have a very small energy, it will have a very large wavelength. If the wavelength is larger than the size of the black hole, then the black hole cannot absorb it. I think this is the mechanism you are looking for.

Maybe but what about gravitational blue shift of the pulse of light as it approaches the black hole?

Maybe but what about gravitational blue shift of the pulse of light as it approaches the black hole?

Good question!

Let us recall that we are trying to explain why the black hole of given mass has a finite information capacity. But a classical black hole, described by a classical continuous field theory, has an infinite information capacity. Indeed, your thought experiment nicely demonstrates it. So finite information capacity must be a consequence of quantum gravity. However, since we do not have a unique and complete theory of quantum gravity, we also do not have a unique and complete answer to your question. At best, we may have a partial answer based on some particular theory of quantum gravity. And we do not know which particular theory of quantum gravity, if any, is the correct one.

So, is there some particular theory of quantum gravity which you would favor in this case?

So, is there some particular theory of quantum gravity which you would favor in this case?

No, I don't have a favorite quantum gravity theory.

Hey I got an idea: In the frame of the black hole the light pulse is long, so it has time to expand before being completely absorbed, so some photons miss the black hole, and those photons missing the target contain more entropy - their directions differ more than those photon's directions that hit the target.